Question

The circumference of a circle is 24π ft. What is the area, in square feet? Express your answer in terms of

π
π.

Answer 1

Given that:

• The circumference of a circle is 24π ft.

To Find:

• What is the area, in square feet?

We know that:

• Circumference of a circle = 2πR
• Area of a circle = πR²

Where,

• Radius is denoted as R.

Finding the radius of the circle:

Circumference of a circle = 24π

⟶ 2πR = 24π

⟶ 2πR = 2π × 12

Cancelling 2π.

⟶ R = 12

∴ Radius of the circle = 12 ft.

Finding the area of the circle:

⟶ Area = πR²

⟶ Area = π(12)²

⟶ Area = π × 12 × 12

⟶ Area = π × 144

⟶ Area = 144π

Hence,

• Area of the circle is 144π square feet.

Answer 2

`144\pi`

Explanation:

Circumference =
`\pi d`

Diameter =
`2r`

Area of a circle =
`\pi r^2`

From our first equation, we can find our value for our diameter:

We do this by dividing
`24 \pi` by
`\pi` to get 24.

`c=\pi d`

`d=(c)/(\pi ) = (24\pi )/(\pi ) =24`

Using our second equation, we can find out the value for our radius:

`d=2r`

`r=(d)/(2) =(24)/(2) =12`

Now we have a value for our radius, we can use our third equation to find out our area:

`A=\pi 12 ^2 = 144 \pi`